From the classical theory of infinite products (see for instance [1]}) the infinite product \(P=\prod _{k=m}^\infty (1+q_k)\) 
of real numbers is said to converge if there is \(N\in \mathbb {Z}_m\)  such that \(1 +q_k \ne 0\)  for \(k\ge N\)  and
\(P_n=\prod _{k=N}^n (1 +q_k)\) 
